What do the following two equations represent? $x-5y = -4$ $x-5y = 4$
Solution: Putting the first equation in $y = mx + b$ form gives: $x-5y = -4$ $-5y = -x-4$ $y = \dfrac{1}{5}x + \dfrac{4}{5}$ Putting the second equation in $y = mx + b$ form gives: $x-5y = 4$ $-5y = -x+4$ $y = \dfrac{1}{5}x - \dfrac{4}{5}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.